1. Field of the Invention
The present invention generally relates to computer-aided engineering analysis of a structure, more particularly to systems and methods of performing vibro-acoustic analysis of a structure subjected to harmonic excitations (i.e., loads).
2. Description of the Related Art
The finite element method (FEM) (sometimes referred to as finite element analysis (FEA)) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations. The solution approach is based either on eliminating the differential equation completely (steady state problems), or rendering the PDE into an approximating system of ordinary differential equations, which are then numerically integrated using standard techniques such as Euler's method, Runge-Kutta, etc.
FEA is becoming increasingly popular with automobile manufacturers for optimizing both the aerodynamic performance and structural integrity of vehicles. Similarly, aircraft manufacturers rely upon FEA to predict airplane performance long before the first prototype is built. Rational design of semiconductor electronic devices is possible with Finite Element Analysis of the electrodynamics, diffusion, and thermodynamics involved in this situation. FEA is utilized to characterize ocean currents and distribution of contaminants. FEA is being applied increasingly to analysis of the production and performance of such consumer goods as ovens, blenders, lighting facilities and many plastic products. In fact, FEA has been employed in as many diverse fields as can be brought to mind, including plastics mold design, modeling of nuclear reactors, analysis of the spot welding process, microwave antenna design, simulating of car crash and biomedical applications such as the design of prosthetic limbs. In short, FEA is utilized to expedite design, maximize productivity and efficiency, and optimize product performance in virtually every stratum of light and heavy industry. This often occurs long before the first prototype is ever developed.
One of the challenging FEA tasks is to simulate acoustic responses (e.g., noises) of a structure subjected to external excitations. The common approaches for solving a structural acoustic response problem involve solving equations in vibration and acoustic analyses. For systems with large number of FEA elements, solving these equations in traditional numerical methods becomes computational intensive and requires large resources.
Over the past decades, boundary element method (BEM) has emerged as a versatile and powerful tool for solving engineering problems. BEM is a numerical method for solving boundary-value or initial-value problems formulated by using boundary integral equations. BEM is advantageous for solving infinite domain problems since the radiation condition at infinity is automatically satisfied. BEM reduces the dimension of the problems by one, e.g. only boundaries of the domain need to be meshed. Thus BEM is presented in many cases as an alternative to the more widely used FEA. Particularly BEM has become a good candidate for solving acoustic problems which are governed by Helmholtz equation.
Many of the prior art approaches to perform vibro-acoustic analysis have been ad hoc, for example, stringing together different computer software. These approaches not only require human intervention, but also are error prone. Therefore, it would be desirable to have integrated methods and systems for performing vibro-acoustic analysis of a structure effectively and efficiently, using both FEA and BEM.